Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Suppose that [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are sets, defined as follows. Find the intersection and union of [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. Enter the elements of the sets in increasing order, separated by commas. If a set is the empty set, just enter DNE inside the braces given.

[tex]\[
\begin{array}{l}
A = \{2, 3, 6, 7\} \text{ and } B = \{1, 2, 3, 6, 7, 8\} \\
A \cap B = \{\square\} \\
A \cup B = \{\square\}
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Given the sets [tex]\( A = \{2, 3, 6, 7\} \)[/tex] and [tex]\( B = \{1, 2, 3, 6, 7, 8\} \)[/tex], we need to determine the intersection and union of these sets.

### Intersection ([tex]\(A \cap B\)[/tex]):
The intersection of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is the set of elements that are common to both [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
- Elements in [tex]\( A \)[/tex]: [tex]\( \{2, 3, 6, 7\} \)[/tex]
- Elements in [tex]\( B \)[/tex]: [tex]\( \{1, 2, 3, 6, 7, 8\} \)[/tex]

The common elements are [tex]\( 2, 3, 6, \)[/tex] and [tex]\( 7 \)[/tex].

Thus, the intersection [tex]\(A \cap B = \{2, 3, 6, 7\}\)[/tex].

### Union ([tex]\(A \cup B\)[/tex]):
The union of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is the set of elements that are in [tex]\( A \)[/tex], in [tex]\( B \)[/tex], or in both.
- Elements in [tex]\( A \)[/tex]: [tex]\( \{2, 3, 6, 7\} \)[/tex]
- Elements in [tex]\( B \)[/tex]: [tex]\( \{1, 2, 3, 6, 7, 8\} \)[/tex]

Combining the elements from both sets (and removing duplicates) gives us: [tex]\( 1, 2, 3, 6, 7, \)[/tex] and [tex]\( 8 \)[/tex].

Thus, the union [tex]\(A \cup B = \{1, 2, 3, 6, 7, 8\}\)[/tex].

### Answer:
[tex]\[ \begin{array}{l} A = \{2, 3, 6, 7\} \\ B = \{1, 2, 3, 6, 7, 8\} \\ A \cap B = \{2, 3, 6, 7\} \\ A \cup B = \{1, 2, 3, 6, 7, 8\} \end{array} \][/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.